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Open AccessArticle

Some New Fractional-Calculus Connections between Mittag–Leffler Functions

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Department of Mathematics and Statistics, University of Victoria, Victoria, BC V8W 3R4, Canada
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Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan
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Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK
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Department of Mathematics, Faculty of Arts and Sciences, Eastern Mediterranean University, Famagusta 99628, TRNC, Mersin-10, Turkey
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Department of Mathematics, Cankaya University, Balgat, Ankara 06530, Turkey
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Institute of Space Sciences, 077125 Magurele-Bucharest, Romania
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Author to whom correspondence should be addressed.
Mathematics 2019, 7(6), 485; https://doi.org/10.3390/math7060485
Received: 30 March 2019 / Revised: 10 May 2019 / Accepted: 20 May 2019 / Published: 28 May 2019
We consider the well-known Mittag–Leffler functions of one, two and three parameters, and establish some new connections between them using fractional calculus. In particular, we express the three-parameter Mittag–Leffler function as a fractional derivative of the two-parameter Mittag–Leffler function, which is in turn a fractional integral of the one-parameter Mittag–Leffler function. Hence, we derive an integral expression for the three-parameter one in terms of the one-parameter one. We discuss the importance and applications of all three Mittag–Leffler functions, with a view to potential applications of our results in making certain types of experimental data much easier to analyse. View Full-Text
Keywords: fractional integrals; fractional derivatives; Mittag–Leffler functions fractional integrals; fractional derivatives; Mittag–Leffler functions
MDPI and ACS Style

Srivastava, H.M.; Fernandez, A.; Baleanu, D. Some New Fractional-Calculus Connections between Mittag–Leffler Functions. Mathematics 2019, 7, 485.

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